In \(\mathbb {R}^3\) , to understand generic mean curvature flow without a low-entropy condition (in contrast with this note), one must work at the first non-generic time rather than globally in space-time. However, two serious issues arrise when working this way. First, there is no partial regularity known for tangent flows pastAt the first singular time, work of Ilmanen [1]} and Wang [2]} completely describe the tangent flows up to the potential occurrence of multiplicity. the first singular time without a low-entropy bound. Second, the possibility that a small perturbation of the initial data increases the first singular time slightly without improving the flow in an effective way. To that end, in [3]} we had to additionally prove that the nearby flows strictly decrease genus as they avoid the non-generic singularity. This genus-loss property is crucial for tackling Huisken's conjecture in \(\mathbb {R}^3\)  without a low-entropy condition and is a consequence of the classification of ancient one sided flows, as obtained in [3]}.
